I'm pretty sure the state of Connecticut is to blame here, not NewEgg. It's not NewEgg's job to violate tax laws on its customers' behalf. If Connecticut-based customers dislike the actions of the state (which I hope they do), it's on them to make that known to the state.
The only language that makes NewEgg look like they are proactively giving up this data comes from a spokesperson for Connecticut itself, who has a vested interest in making it look like NewEgg is to blame, not the state.
They chose to give their records to the government which causes a major hassle for those users (and increases the likelihood that those records get breached, infringing on users' privacy). They did this at the expense of potentially hurting future Newegg sales because they'll have to honestly show users the tax while they are buying things, rather than having the government hunt down users later on.
Newegg and all companies that exist within the confines of the US national borders have a legal requirement to do certain things. This is no different to what the citizens are legally required to do.
If the state imposes a "use tax" on your purchases then you are required to follow that up. If the legal requirements are that companies are to give the purchase records to the state authorities, then that is what will happen.
Just because you find it objectionable is irrelevant.
However, if you want to start a grass-roots objection to these tax regimes then start with your local, state and federal politicians. Make it plain that they will no longer be getting the popular vote and that their cushy jobs will be taken from them permanently.
But, as you most likely know this will not happen and the situation will not change as the general populous has no interest in the matter.
“Following tax laws”